Not accepting resignation even after ready to serve notice period

Dear sir, I am working with one Pvt Ltd company as a Team leader/IT support engineer. My job location is Mumbai (Client end) & my payroll company head office is in Bangalore. I am working with my payroll company since last 2.5 years. Now I am a father of a baby girl and the salary I'm getting from my current company is not sufficient so I searched and found good opportunity outside my organization. As per my offer letter I have to serve two months of notice period if I do resign from the job. I've resigned on 10th November and ready to serve two months notice period but my reporting manager and Operation manager are not ready to accept my resignation as they are saying that they didn't expect resignation from me but not giving me any official reason. Now as per 2 months notice period my LWD would fall on 9th January and I've committed to new company that I'll join their company from 10th January. I've discussed the same with my current managers but they are not ready to listen at all and simply saying that they cannot accept my resignation letter and now they are not answering my call also. Now I am worried about my relieving letter as this one is my first job in IT and I can't just ignore my reliving letter. Due to this kind of issues I am very much in tension as my future is depending on this. What if they don't accept my resignation till LWD and not providing me reliving letter. Please give me advise on this as I am not able to concentrate on my work due to this. FYI... I've not signed any employment contract. Thanks in Advance. Arpan